Solve for $x$ and $y$ using elimination. ${-4x-y = -46}$ ${-5x+y = -35}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-9x = -81$ $\dfrac{-9x}{{-9}} = \dfrac{-81}{{-9}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-4x-y = -46}\thinspace$ to find $y$ ${-4}{(9)}{ - y = -46}$ $-36-y = -46$ $-36{+36} - y = -46{+36}$ $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ You can also plug ${x = 9}$ into $\thinspace {-5x+y = -35}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ + y = -35}$ ${y = 10}$